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Jason228
@Jason228
June 2022
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Найти значение производной в точке х0
f(x)=(2x^2+1)(4+x^3), x0=1
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Verified answer
F(x) = (2x² + 1)(4 + x³)
f '(x) = (2x² + 1)' * (4 + x³) + (2x² + 1)(4 + x³)' = 4x(4 + x³) + (2x² + 1) * 3x² =
= 16x + 4x⁴ + 6x⁴ + 3x² = 10x⁴ + 3x² + 16x
f '(x₀) = f '(1) = 10 * 1⁴ + 3 * 1² + 16 * 1 = 10 + 3 + 16 = 29
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Answers & Comments
Verified answer
F(x) = (2x² + 1)(4 + x³)f '(x) = (2x² + 1)' * (4 + x³) + (2x² + 1)(4 + x³)' = 4x(4 + x³) + (2x² + 1) * 3x² =
= 16x + 4x⁴ + 6x⁴ + 3x² = 10x⁴ + 3x² + 16x
f '(x₀) = f '(1) = 10 * 1⁴ + 3 * 1² + 16 * 1 = 10 + 3 + 16 = 29